Algebra 2
Name ______________________________
Test Unit 4: Matrices & Systems of Equations
Class Period _______________
1.
Hamburger Heaven sells burgers for $3 and cheeseburgers for $4. On day at lunch, they sold 10
more cheeseburgers than hamburgers and made $215. Write a system of equations that could be
used to find the number of burgers, b, and cheeseburgers, c, that the shop sold that day? Solve
using matrices. 3b + 4c = 215
burgers = 25
b + 10 = c
cheeseburgers = 35
2.
The length of a rectangle is equal to double the width. Write a system of equations that can be
used to find the dimensions of the rectangle if the perimeter is 72 centimeters? Solve using
matrices.
L = 2W
2L + 2W = 72
3.
24 = Length
12 = Width
Sketch the graph of the system of linear inequalities
TEK2A.3AB:
3x + y > -3
2y – 4x > 0
y > 2x
y > -3 – x
4.
IF X =[
TEK2A.3B
2 −4
] find the inverse matrix, X-1
3 −1
Use a matrix equation to solve each of the following. Write linear system in matrix form for full credit
TEK2A.3B
5.
x  2 y  6

 x  y  3
(0, 3)
6.
2 x  y  13

x  y  5
(6, 1)
Use a matrix equation to solve each of the following. Write the linear system in matrix form for full
credit
7.
TEK2A.3B
 x  y  z  4

 x  y  3z  1
x  2 y  z  4

x = 19.5
y = -13
z = -10.5
9.
8.
2 x  4 y  2 z  16

 2 x  5 y  2 z  34
x  2 y  2z  4

x=8
y = -2
z = -4
Sally is investing some money to save for a car. She puts some of it in a savings account with 3%
interest, and then she puts the rest in a checking account with 1% interest. At the end of the year, she
earns $110 total interest. How much money did she invest in each account if she had $5,000 to invest?
TEK2A.3A
X = Inv #1
Y = Inv #2
x+
y = 5000
.01 x + .03y = 110
Inv #1 = $2000
Inv #2 = $3000
10. Chuck is buying supplies for his painting business. Last week, he purchased 12 brushes and 4 pails for
$72. This week, he bought 8 brushes and 2 pails for $46. Assuming prices for each item remain
constant, how much will he pay for next week’s order of 5 buckets and 3 pails? TEK2A.3A
b = brushes
p = pails
12b + 4p = 72
8b + 2p = 46
Brushes = $5
Pails = $3
Next week’s order of 5 buckets and 3 pails will cost $34.00
11. At least 1600 movie tickets were sold on opening night. General admission was $9 while matinee rates
were discounted 20% off the general admission price. Box office receipts totaled more than $13,500. Is
it possible to have sold 1,000 general admission tickets and 750 matinee tickets? Justify your answer.
TEK2A.3A
X = general price which is $9.00
Y = matinee price which is $7.20
x + y ≥ 1600
9x + 7.2 y > 13,500
Yes, it is possible to have sold 1,000 general admission tickets and 750 matinee tickets.
Justification: 1000 + 750 ≥ 1600
17500 ≥ 1600 TRUE
9(1000) + 7.2(750) > 13,000
14,400 > 13,000